biblio.bib

@unpublished{NABES09,
  abstract = {{W}e obtain non asymptotic bounds for the {M}onte {C}arlo algorithm associated to the {E}uler discretization of some diffusion processes. {T}he key tool is the {G}aussian concentration satisfied by the density of the discretization scheme. {T}his {G}aussian concentration is derived from a {G}aussian upper bound of the density of the scheme and a modification of the so-called ``{H}erbst argument'' used to prove {L}ogarithmic {S}obolev inequalities. {W}e eventually establish a {G}aussian lower bound for the density of the scheme that emphasizes the concentration is sharp.},
  affiliation = {{L}aboratoire de {P}robabilit{\'e}s et {M}od{\`e}les {A}l{\'e}atoires - {PMA} - {CNRS} : {UMR}7599 - {U}niversit{\'e} {P}ierre et {M}arie {C}urie - {P}aris {VI} - {U}niversit{\'e} {P}aris-{D}iderot - {P}aris {VII}},
  author = {{L}emaire, {V}incent and {M}enozzi, {S}tephane},
  date-added = {2010-01-12 13:52:52 +0100},
  date-modified = {2010-01-12 20:14:38 +0100},
  keywords = {{N}on asymptotic {M}onte {C}arlo bounds, {D}iscretization schemes, {G}aussian concentration},
  language = {{A}nglais},
  title = {{O}n some {N}on {A}symptotic {B}ounds for the {E}uler {S}cheme},
  url = {http://hal.archives-ouvertes.fr/hal-00445494/en/},
  year = {2009},
  bdsk-url-1 = {http://hal.archives-ouvertes.fr/hal-00445494/en/}
}

@unpublished{JMGE08,
  abstract = {{T}he recent liberalization of the electricity and gas markets has resulted in the growth of energy exchanges and modelling problems. {I}n this paper, we modelize jointly gas and electricity spot prices using a mean-reverting model which fits the correlations structures for the two commodities. {T}he dynamics are based on {O}rnstein processes with parameterized diffusion coefficients. {M}oreover, using the empirical distributions of the spot prices, we derive a class of such parameterized diffusions which captures the most salient statistical properties: stationarity, spikes and heavy-tailed distributions. {T}he associated calibration procedure is based on standard and efficient statistical tools. {W}e calibrate the model on {F}rench for electricity and on {UK} market for gas, and then simulate some trajectories which reproduce well the observed prices behavior. {F}inally, we illustrate the importance of the correlation structure and of the presence of spikes by measuring the risk on a power plant portfolio.},
  affiliation = {{L}aboratoire de {P}robabilit{\'e}s et {M}od{\`e}les {A}l{\'e}atoires - {PMA} - {CNRS} : {UMR}7599 - {U}niversit{\'e} {P}ierre et {M}arie {C}urie - {P}aris {VI} - {U}niversit{\'e} {D}enis {D}iderot - {P}aris {VII}},
  author = {{F}rikha, {N}oufel and {L}emaire, {V}incent},
  date-modified = {2010-01-12 13:53:54 +0100},
  language = {{A}nglais},
  title = {{J}oint {M}odelling of {G}as and {E}lectricity spot prices},
  url = {http://hal.archives-ouvertes.fr/hal-00421289/en/},
  year = {2009},
  bdsk-url-1 = {http://hal.archives-ouvertes.fr/hal-00421289/en/}
}

@unpublished{URIS08,
  abstract = {{W}e propose an unconstrained stochastic approximation method of finding the optimal measure change (in an a priori parametric family) for {M}onte {C}arlo simulations. {W}e consider different parametric families based on the {G}irsanov theorem and the {E}sscher transform (or exponential-tilting). {I}n a multidimensional {G}aussian framework, {A}rouna uses a projected {R}obbins-{M}onro procedure to select the parameter minimizing the variance. {I}n our approach, the parameter (scalar or process) is selected by a classical {R}obbins-{M}onro procedure without projection or truncation. {T}o obtain this unconstrained algorithm we intensively use the regularity of the density of the law without assume smoothness of the payoff. {W}e prove the convergence for a large class of multidimensional distributions and diffusion processes. {W}e illustrate the effectiveness of our algorithm via pricing a {B}asket payoff under a multidimensional {NIG} distribution, and pricing a barrier options in different markets.},
  affiliation = {{L}aboratoire de {P}robabilit{\'e}s et {M}od{\`e}les {A}l{\'e}atoires - {PMA} - {CNRS} : {UMR}7599 - {U}niversit{\'e} {P}ierre et {M}arie {C}urie - {P}aris {VI} - {U}niversit{\'e} {D}enis {D}iderot - {P}aris {VII}},
  author = {{L}emaire, {V}incent and {P}ag{\`e}s, {G}illes},
  date-modified = {2010-01-12 13:53:34 +0100},
  keywords = {{S}tochastic algorithm ; {R}obbins-{M}onro ; {I}mportance sampling ; {E}sscher transform ; {G}irsanov ; {NIG} distribution, {B}arrier options},
  language = {{A}nglais},
  note = {To appear in Annals of Applied Probability},
  title = {{U}nconstrained {R}ecursive {I}mportance {S}ampling},
  url = {http://hal.archives-ouvertes.fr/hal-00293466/en/},
  year = {2008},
  bdsk-url-1 = {http://hal.archives-ouvertes.fr/hal-00293466/en/}
}

@article{ESAIM07,
  abstract = {{T}he aim of this short note is to study the behavior of the weighted empirical measures of the decreasing step {E}uler scheme of a one{-}dimensional diffusion process having multiple invariant measures. {T}his situation can occur when the drift and the diffusion coefficient are vanish simultaneously.},
  author = {Lemaire, Vincent},
  doi = {10.1051/ps:2007018},
  issn = {1292-8100},
  journal = {ESAIM. Probability and Statistics},
  mrclass = {60H10 (60J60 65C30)},
  mrnumber = {MR2320818 (2008h:60228)},
  mrreviewer = {Vigirdas Mackevi{\v{c}}ius},
  pages = {236--247},
  title = {Behavior of the {E}uler scheme with decreasing step in a degenerate situation},
  volume = {11},
  year = {2007},
  bdsk-url-1 = {http://dx.doi.org/10.1051/ps:2007018}
}

@article{SPA07,
  abstract = {{W}e propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally {L}ipschitz. {U}nder this assumption, a regular explicit {E}uler scheme (with constant or decreasing step) may explode and implicit {E}uler schemes are {CPU}-time expensive. {T}he algorithm we introduce is explicit and we prove that any weak limit of the weighted empirical measures of this scheme is a stationary distribution of the stochastic differential equation. {S}everal examples are presented including gradient dissipative systems and {H}amiltonian dissipative systems.},
  author = {Lemaire, Vincent},
  coden = {STOPB7},
  doi = {10.1016/j.spa.2007.02.004},
  issn = {0304-4149},
  journal = {Stochastic Processes and their Applications},
  mrclass = {60J60 (60H35 65C30)},
  mrnumber = {MR2353037 (2008k:60189)},
  mrreviewer = {Madalina Deaconu},
  number = {10},
  pages = {1491--1518},
  title = {An adaptive scheme for the approximation of dissipative systems},
  volume = {117},
  year = {2007},
  bdsk-url-1 = {http://dx.doi.org/10.1016/j.spa.2007.02.004}
}